The direct estimators \(\hat{\theta }_i^{\mathrm {d}}\)  of the domain proportions can be improved using the FH model [1]}. The data for this domain-level model are the estimates \(\hat{\theta }_i^{\mathrm {d}}\) , their corresponding estimates \(\hat{\psi }_i\)  of the sampling variances \(\psi _i=\operatorname{{var}_{p}}(\hat{\theta }_i^{\mathrm {d}})\) , and the covariates \(\mathbf {z}_i\) , \( i=1,\ldots , M\) . The basic FH model consists of two parts, see [2]}, that are combined into the linear mixed model
\(\hat{\theta }_i^{\mathrm {d}}=\mathbf {z}_i^{\prime } +v_i+\varepsilon _i, \qquad i=1,\ldots , M,\) 
